One of the principle drawbacks of multicarrier digital and/or analogue communication systems such as wired, wireless and optical systems is their sensitivity to frequency and sampling frequency synchronizations errors. A frequency offset or a frequency mismatch between a transmitter and a receiver usually results in a frequency offset prior to a received signal being demodulated. In e.g. orthogonal frequency division multiplexing (OFDM) systems, the frequency mismatch increases inter-carrier interference (ICI) and additionally a constant phase rotation is introduced for every symbol received. This impairment results in degraded performance of the receiver. In a publication by Pollet et al entitled: “The BER Performance of OFDM Systems using Non-Synchronised Sampling”, IEEE Global Telecommunications Conference 1994, pp 253-257, it is shown that a 1% frequency mismatch, relative to the subcarrier spacing in an OFDM symbol, can be tolerated for a negligible 0.5 dB loss in 64 QAM (quadrature amplitude modulation), whereas QPSK (quadrature phase shift keying) modulation can tolerate up to a 5% error, and as such requires a tracking of sampling frequency offset. A frequency offset also results in degradation of the performance of a DC (direct current) offset and time synchronizer algorithms at the receiver. Furthermore, degradation of an estimation of a channel via which signals are received, is experienced especially in systems where multiple signals or multiple symbols are combined together to produce a channel estimate e.g. space time block coding (STBC), spatial division multiplexing (SDM) and multiple input multiple output (MIMO) systems.
As mentioned earlier, multicarrier systems are also sensitive to a sampling frequency error or mismatch between a transmitter and a receiver. In e.g. OFDM systems, mismatch in sampling frequencies between a transmitter and a receiver can lead to the loss of orthogonality between subcarriers which results in an increase in ICI. Additionally, an increasing phase rotation is introduced which increases proportionally as the subcarrier frequency increases (i.e. the outer subcarriers are affected more than the inner subcarriers) and also as consecutive OFDM symbols are received. This impairment continues to increase until the receiver can no longer correctly decode the received signal, and as such requires the tracking of the sampling frequency offset. In a publication by Heiskala & Terry, entitled: “OFDM Wireless LANS: theoretical and practical guide”, Chapter 2, SAMS, December 2001, it has been shown that for very long OFDM packets, a sampling frequency mismatch can advance or retard the optimal time synchronization point by an integer sample period or more.
The frequency mismatch and the sampling frequency mismatch between a transmitter and a receiver can be estimated by existing synchronisation algorithms suggested in the above cited publication. As an example, a frequency mismatch can be estimated based on known training information embedded into the transmitted signal e.g. a preamble and pilot subcarriers or based on analyzing the received signal or based on inherent characteristics of a received signal e.g. a cyclic prefix in case of a received OFDM signal.
However, in actual implementation, the estimated frequency offset does not generally equal the actual frequency error because of the influence of noise and analog impairment components between the transmitter and the receiver on the estimation algorithms. Therefore, a residual frequency error, which is defined as the difference between the estimated frequency error and the actual frequency error, exists. The presence of the residual frequency error will affect system performance in terms of a reduction in the signal to noise ratio of the receiver and a rotation of a constellation. The constellation rotation is related to the residual frequency error according to the following approximation: Constellation Rotation per symbol)≈360×fresidual×Ts (degrees), where Ts is the period of e.g. an OFDM symbol. Higher order modulations, such as 64 QAM, are particularly sensitive to the constellation rotation as the subcarrier constellation ends up being rotated over the decision boundaries and hence correct demodulation becomes more difficult. The residual frequency error can also be significant for lower order modulations that have longer packet lengths. Long packet lengths allow the constellation to progressively rotate over time, until the subcarrier constellation is eventually rotated across the decision boundary, making correct demodulation more difficult.
In the prior art, the amount (or accuracy) of the residual frequency mismatch usually depends on the algorithm employed. An example of such prior art can be found in a publication by V. S. Abhayawardhana et al, “Residual Frequency Offset Correction for Coherently Modulated OFDM systems in Wireless Communication”, Vehicular Technology Conference, 2002. VTC Spring 2002. IEEE 55th, Volume 2, 6-9 May 2002 Page(s):777-781 vol. In this prior art, a residual frequency correction algorithm is used to continuously track and compensate for the residual frequency error that is present after an acquisition of an estimate of the frequency offset using another algorithm known as the Schmidl and Cox Algorithm (SCA). The residual frequency error is estimated by tracking the rate of phase change at the output of a frequency domain equalizer (FEQ) following the fast Fourier transform (FFT) operation. However, the estimate of the residual frequency error can be seriously affected by subchannels with a low SNR resulting from spectral nulls in the channel response. Therefore, a threshold is, in this prior art, introduced to select subchannels with a magnitude that is higher than the threshold. Thus not all the available information is being used and as such the performance is will be degraded dependent on the level of the threshold chosen. This prior art therefore can be said to suffer from a threshold effect.
In another technique described in M Sliskovic: “Sampling Frequency Offset Estimation and Correction in OFDM systems”, The 8th IEEE International Conference on Electronics, Circuits and Systems, 2001. Volume 1, 2-5 Sep. 2001 Page(s):437-440, the phase difference between successive symbols is used to estimate the frequency offset, which can equally be used to estimate the residual frequency error. The proposed technique involves repetition of data symbols and comparison of the phases between successive repeated symbols on all subcarriers. In this prior art, when the phase difference is small (less than 1 degree), then an arg (or arctan) function can be approximated by a linear function, e.g. α=arg(a+jb)=arctan(b/a)≈b/a or sin(2πx)≈2πx The problem with utilising such an approximation is that as the angle gets larger the approximation becomes worse, and the result will lead to poorer quality residual frequency estimate, which will mean that the correction applied will be in error. This is significant for 64 QAM constellations where an error in the order of degrees will degrade the receiver performance. Additionally the angle is not constrained to small angles (it can be shown to lie anywhere between 0 and 360 degrees) since it is dependent on the channel model (SNR and delay spread) and the amount of impairments in the system (phase noise, phase and amplitude imbalance, DC offset, crystal tolerance etc) and as such the small angle approximation leads to an incorrect estimation and correction which will lead to degraded performance of the receiver. The prior art also introduces a technique to avoid the threshold effect, by weighting the phase errors of each subcarrier by a value proportional to the SNR. The SNR of each subcarrier can be estimated by the square of the channel estimate denoted here ĤĤ*. However, at low SNR the square of the channel estimate is not accurate.
In the above mentioned prior art, an approximation has been made where the sampling frequency offset is assumed to be zero. In non-flat fading channels or flat fading channels where the subcarriers used are not symmetrical, such an approximation will mean that the phase estimate will contain an additional error component caused by neglecting the sampling frequency offset.